Answer
$2x\ln x-x^2+C$
Work Step by Step
We will solve the given integral by using integrate-by-parts formula such as: $\int udv=uv-\int v du$
$\displaystyle \int \ln (x^2) \ dx=2 \int \ln x \ dx$
Here, $u=\ln x$ and $dv=2dx \implies v=2x$
$ \int \ln x (2) \ dx=\ln x (2x) -\int 2x \ dx$
Therefore, we have:
$\displaystyle \int \ln (x^2) \ dx=2x\ln x-x^2+C$
